Method for making composite utility pole

ABSTRACT

A hollow, tapered, fiber-reinforced plastic utility pole, and a method for making the pole. The pole is designed by a computer-modelling technique that simulates applying resin-coated, reinforcing strands over the outer surface of a mandrel. A plurality of test stations are incrementally spaced from the tip portion to the butt portion of the pole simulated on the mandrel. The thickess-to-diameter ratio must be equal to or greater than an established constant at each station or additional circuits of resin-coated, reinforcing strands deemed to have been applied, as required. One then calculates the stress resistance at each successive station to determine if the acceptable stress is greater than the stress resistance required. Whatever additional circuits of resin-coated, reinforcing strands are necessary are then deemed to have been applied. One then calculates the projected failure load in response to the deflection calculated to occur in response to the rated load at each station to determine if the actual loading to be applied to the pole in relation to the projected failure load at that station is acceptable. The acceptable stress is modified by a binary chopping routine until the relation of the projected failure load and the rated load differ by an acceptable amount. All tests are recalculated until no further changes are require. The pole may then be laid up on a mandrel, and the resin cured to complete the pole.

TECHNICAL FIELD

The present invention relates generally to utility poles. Moreparticularly, the present invention relates to utility poles made ofcomposite materials such as fiber reinforced plastic (FRP).Specifically, the present invention relates not only to a method formaking FRP utility poles with the minimal amount of FRP materials toprovide the desired, preselected strength but also to a pole made bysuch a method.

BACKGROUND OF THE INVENTION

Electrical transmission wires, telephone wires and lighting fixtures areoften supported on utility poles. Such poles must be capable ofwithstanding not only the columnar load applied by the weight of theobjects supported thereon but also the bending load imposed by eccentricloading and by wind. As a general rule, wooden, concrete or steel poleshave historically been used for this purpose. These poles are all heavy,and each presents some unique disadvantages.

Wooden poles, for example, are subject to rot--i.e.: decomposition fromthe action of bacteria or fungi--and pest attack--i.e.: wood borers andpecking fowl. Unfortunately, wooden poles are likely to rot at and belowthe ground surface which can result in a pole collapsing, or toppling,sometimes without warning. To help combat this type degradation thepoles are typically treated with chemicals which are intended to prolongthe useful life of the wooden pole. However, the chemical preservativescan leach out of the poles and contaminate the local ground water.Moreover, chemical preservatives are not permanent, and it is extremelydifficult, if not impossible, effectively to treat wooden poles in thefield.

Steel poles are subject to rust and therefore need constant attentionand maintenance. The rust proofing compounds used can also have adeleterious effect on the environment. Even if the environmentalproblems could be solved, steel poles are heavy and are not easilymanipulated. Moreover, steel poles are electrically conductive, and eventhough extreme care may be taken to insulate the electrical fixturesfrom the pole, routine storm damage can result in the pole becomingelectrified. Finally, steel poles are an expensive inventory item.

Concrete poles are even heavier than steel poles. As a result, theexpense of transporting and handling concrete utility poles can beexcessive. They are, therefore, often constructed in fairly closeproximity to the erection site. Concrete poles, like the aforementionedwooden and steel poles, are also subject to the ravages of theenvironment, particularly the freezing and thawing cycles which existacross massive geographic areas of the U.S.

Fiber reinforced plastic (FRP) poles have been suggested as an excellentreplacement for wooden, steel and/or concrete poles because they are notas subject to the same deficiencies. For example, FRP composite polesprovide a basic electrical insulation level that is greater than wooden,steel or concrete poles, and that basic electrical insulation level ismaintained over the life of the FRP pole. Moreover, FRP utility polesprovide an extremely favorable strength-to-weight ratio. FRP utilitypoles are generally comprised of several layers of fiber reinforcedresin laminate. The fibers normally employed are glass, graphite, boronor other exotic materials, or combinations thereof, which have a Young'smodulus on the order of at least about 10×10⁶ psi (6.9×10¹⁰ N/m²)--wellsufficient to provide the hoop strength and stiffness necessary toprevent buckling and circular deformation of the shaft when under theloads typically imposed on utility poles.

FRP poles are also environmentally safe inasmuch as there is no leachingof chemicals into the soil. FRP poles, unlike their wooden counterpartsdo not require initial, or future, treatment with chemicalpreservatives. Conversely, the FRP composite utility poles possess aninherent resistance to attack from various chemicals that may betypically found in the soil.

However, the prior art FRP poles have proven to be too expensive.Typically, FRP poles are made by laying up resin coated fiberglass, orother high modulus strands, on a tapered mandrel. When the reinforcingfilaments are wound on a tapered mandrel, the resulting tapered, tubularpole has a greater wall thickness at the tip portion of the pole than itdoes at the butt portion. Tubular FRP poles fabricated in this manner dopossess high cantilever strength through the tip portion, where the wallthickness is greater and the outside diameter is smaller. However, inorder to obtain tubular poles that have sufficient cantilever strengthnear the butt portion, excessive amounts of materials are amassed in thetip portion, thus unnecessarily increasing the cost and weight of thepole.

SUMMARY OF THE INVENTION

It is, therefore, a primary object of the present invention to providean improved utility pole having a contour that convergingly tapers fromthe base, or butt, portion to the tip portion of the pole withoutsignificantly decreasing the wall thickness along the butt portion tothe detriment of the pole strength or increasing the wall thicknessalong the tip portion in excess of what is required to provide thedesired pole strength along the overall length of the utility pole.

It is another object of the present invention to provide an improved,tapered, lightweight, FRP utility pole, as above, that is in the rangeof from approximately one third (1/3) to one half (1/2) the weight ofthe same length pole constructed with wood, steel or concrete.

It is a further object of the present invention to provide an improved,tapered, lightweight, FRP utility pole, as above, that includessuccessively concentric FRP layers, some of which have a length lessthan the total length of the pole.

It is yet another object of the present invention to provide an improvedutility pole, as above, having a wall thickness to pole diameter ratiothat is greater than, or equal to, 0.015 and a beam strength, at anycross section along the length of the pole, that will resist apredetermined, allowable stress.

It is also a primary object of the present invention to provide a methodfor fabricating an FRP utility pole having the foregoingcharacteristics.

These and other objects of the invention, as well as the advantagesthereof over existing and prior art forms, which will be apparent inview of the following detailed specification, are accomplished by meanshereinafter described and claimed.

A tapered, tubular FRP utility pole fabricated in accordance with theconcepts of the present invention has a plurality of fiber-reinforcedplastic layers applied, as required, along a determinable length of thepole in a manner that optimizes the columnar as well as the cantileverstrength of the pole and minimizes the amount of material used. Becausean understanding of the terminology employed is critical to anunderstanding of the present invention, it should be understood that theapparatus which simultaneously encases the outer periphery of themandrel with a plurality of resin-coated, reinforcing fibers, orstrands, does so by relative axial movement between a mandrel and a headwhich directs the resin-coated, reinforcing strands onto the mandrel.That relative movement between the head and the mandrel which applies asingle circumferential application of the reinforcing strands along thelength of the mandrel is deemed a "pass", or "traverse". When therelative movement is reversed to effect a second pass, or traverse, thetwo passes are deemed to constitute one "cycle", or "circuit". Those oneor more circuits, or cycles, which reciprocate through a common lengthalong the mandrel, including any and all underlying portions ofpreviously applied circuits, result in a "layer" of fiber-reinforcedplastic.

With this background it can be stated that at least one, and perhapsmore, FRP circuit normally extends the complete length of the pole.Other circuits will normally extend from the base, or butt, portion ofthe pole for successively lesser lengths to terminate at predetermineddistances from one end or the other of the pole. The resulting shortercircuits, or cycles, combine with the underlying portions of previouslyapplied circuits to provide additional layers, and those layers do notcontribute to an unnecessarily thicker wall along the tip portion incomparison to the thickness of the wall along the base, or butt,portion.

According to prior art techniques widely known and used by the industry,one or more strands, or filaments, of the reinforcing material is woundonto the mandrel, beginning at one end thereof, in a helicalconfiguration of one hand, and one or more successive strands, orfilaments, is wound, beginning at the other end thereof, onto themandrel in a helical configuration of opposite hand. These steps arethereafter repeated until the mandrel is covered with the desired numberof layers. Thereafter, the member is cured.

A representative apparatus for making FRP members is disclosed in U.S.Pat. No. 4,089,727 issued on May 16, 1978, in the name of P. H. McLainand is owned by the assignee of the present invention. The apparatusdisclosed in the '727 patent is described as applying a relativelynarrow ribbon of resin-coated material on each pass, but by modifyingthe head a sufficient number of reinforcing strands may besimultaneously applied circumferentially about the mandrel in order tocover the mandrel completely in only one pass. Successive passes, then,effect only the thickness of the FRP member being made.

During the winding operation there is, therefore, relativerotational--as well as relative longitudinal--movement between themandrel and the winding head.

It is possible to rotate the winding head while rotating, or notrotating, the mandrel. It is also possible to rotate the mandrel whilenot rotating the winding head. Similarly, the relative longitudinalmovement between the winding head and the mandrel can be effected bymovement of either, or both, said members. All variations effect thedesired relative rotation and translation between the winding head andthe mandrel.

The concepts with respect to which the present invention is achieved arenot limited to adoption with any particular means for effecting relativelongitudinal and/or rotational movement. As such, and purely for thesake of simplicity, the prior art and the present invention shall bothhereafter be explained in terms of the situation where the winding headdoes not rotate but is moved longitudinally along the mandrel and themandrel does rotate but does not itself move longitudinally.

As the mandrel is thus rotated, and the winding head is movedlongitudinally therealong, a plurality of reinforcing strands may belaid onto virtually the entire outer periphery of the mandrel rearwardlyof the head as the head traverses longitudinally along the mandrel.

In accordance with the present invention the length of each layer ispredetermined by comparing the cantilever strength with the columnarstrength of the layer at preselected test stations spaced longitudinallyalong the length of a computer-modelled pole.

Equations for mathematically calculating the cantilever strength of atubular pole as well as the critical columnar loading thereof both relyon the moment of inertia of the column and the modulus of the materialfrom which the pole is fabricated. The dimensions of the pole must alsobe such that the ratio of the wall thickness to the inside diameter ofthe pole is equal to, or greater than, 0.015.

Once this ratio of wall thickness to inside diameter is satisfied, thestress resistance at the test station is calculated to ensure that apredetermined maximum stress is not exceeded. If the calculated stressexceeds an acceptable, predetermined, maximum stress, anothercycle--i.e.: a to-and-fro pass, or traverse--of the resin-coated,reinforcing strands is provisionally added, and the new stressresistance level is calculated. Only when the two tests are satisfieddoes the location of the test station move incrementally closer to thebutt of the computer-modelled pole. If the tests are also satisfied atthe next test station, the test station is moved incrementally to thenext successive test station, and when any additional material isrequired another circuit is provisionally added and that test section isretested. This process is repeated for the length of the proposed poleand results in a tapered tubular configuration that will have aplurality of FRP layers, many of which extend along less than the totallength of the modelled pole.

Thereafter the tip deflection of the computer-modelled pole is evaluatedto determine a projected failure load. Differences between the ratedload and the projected failure load of more than a preselected modestvalue (ε) --which may typically be on the order of about one hundred(100) pounds--determine incremental adjustments to the maximum allowablestress. The maximum allowable stress is adjusted by successiveiterations, and comparison, of the rated load with respect to theprojected failure load, at all stations, until such time as the ratedloading F_(R) is less than the projected failure loading F_(P) and theprojected failure loading F_(P) is less than the rated loading F_(R)plus the preselected modest value ε. That is, F_(R) <F_(P) <F_(R) +ε.This sequential recalculation--termed binary chopping--eventuallyconverges on the most desirable number and length of circuits to providethe desired failure load with the minimum weight of the pole. Theforegoing procedure may be readily accomplished on a computer for eachselected station, and an actual pole may then be constructed inconformity with the computer-modelled result. Once the number of layersand their lengths are established for a particular length of pole to besubjected to a specific load, that pole can be readily replicated at anyfuture time without the necessity to repeat the computer-modelling.

A lightweight FRP utility pole constructed in accordance with thepresent invention will provide structures that are in the range of onethird (1/3) to one half (1/2) the weight of the same length poleconstructed with wood, steel or concrete. Moreover, a pole constructedin accordance with the present invention will be environmentallyfriendly inasmuch as none of the materials used to fabricate the polewill leech into the soil. Also, the poles will not need initial orfuture treatment with preservatives.

These FRP poles will have a basic, electrical insulating characteristicthat is more favorable than provided with wooden, concrete or steelpoles. This basic electrical insulating characteristic is maintainedover the life of the pole. The FRP poles have a better resistance toattack from the chemicals that may already be in the soil and resistanceto attack by wood pests such as wood borers, fungus, bacteria or peckingfowl is also provided.

The pole is laid-up on a tapered mandrel by applying successive circuitsof resin-coated, fiber reinforcing strands in which the fibers are woundat approximately a fifteen degree (15°) helix. Each circuit is comprisedof two passes, or traverses, of the resin-coated, fiber reinforcingstrands, with each successive traverse applying the reinforcing strandsin a helix disposed in an opposite hand than that resulting from theprevious traverse. The required support strength is a known value suchthat the stress in the pole can be calculated at any location along thelength of the pole by using the well known formula: ##EQU1## ashereinafter explained in detail.

Because the maximum allowable stress for the FRP material is known,another circuit of FRP can be added between the butt portion and thetest station at which the thickness of the layer was calculated to beinsufficient to pass both tests. This process is continued atsuccessive, predetermined test stations--i.e.:typically every six inches(15.24 cm)--along the length of the pole. It has been found, forexample, that a thirty-five foot (10.67 m) pole which possess mid-rangestrength (when compared to the well known, fifteen classes of strengthfor wooden poles) requires the application of successively shortercircuits to provide three distinct layers.

In order to test the utility poles for columnar strength as well ascantilever strength it has been found that one can predict thecantilever failure load without testing to failure by using poledeflection data, as will also be hereinafter described in detail.

To acquaint persons skilled in the arts most closely related to thepresent invention, one preferred embodiment of an FRP utility pole thatillustrates a best mode now contemplated for putting the invention intopractice is described herein by, and with reference to, the annexeddrawings that form a part of the specification. An exemplary utilitypole as well as the method of making such a pole are described in detailwithout attempting to show all of the various forms and modification inwhich the invention might be embodied. As such, the embodiment shown anddescribed herein is illustrative, and as will become apparent to thoseskilled in these arts, can be modified in numerous ways within thespirit and scope of the invention; the invention being measured by theappended claims and not by the details of the specification.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a side elevation, partly broken away and segmented, of a priorart, FRP, utility pole;

FIG. 2 is an enlarged portion of FIG. 1 taken at the area designated"SEE FIG-2" in FIG. 1;

FIG. 3 is an enlarged portion of FIG. 1 taken at the area designated"SEE FIG-3" in FIG. 1;

FIG. 4 is a side elevation, partly broken away and segmented, of autility pole incorporating the present invention;

FIG. 5 is an enlarged portion of FIG. 4 taken at the area designated"SEE FIG-5" in FIG. 4;

FIG. 6 is an enlarged transverse section of FIG. 5 taken substantiallyalong line 6--6 of FIG. 5;

FIG. 7 is an enlarged portion of FIG. 4 taken at the area designated"SEE FIG-7" in FIG. 4;

FIG. 8 is an enlarged portion of FIG. 4 taken at the area designated"SEE FIG-8" in FIG. 4;

FIG. 9 is an enlarged, end elevation taken substantially along line 9--9of FIG. 4 and depicting a view from the tip, or top, portion of the poletoward the base, or butt, portion;

FIG. 10 is an enlarged side elevation, partly broken away, takensubstantially along line 10--10 of FIG. 4;

FIG. 11 is an enlarged, transverse section taken substantially alongline 11--11 of FIG. 4;

FIG. 12 is an enlarged, side elevation, partly broken away, takensubstantially along line 12--12 of FIG. 4;

FIG. 13 is an enlarged, transverse section taken substantially alongline 13--13 of FIG. 4;

FIG. 14 is an enlarged side elevation, partly broken away, takensubstantially along line 14--14 of FIG. 4;

FIG. 15 is a diagrammatic representation of the tip portion of a utilitypole assembled on a mandrel;

FIG. 16A is a portion of a flow chart for an algorithm that may be usedin computer-modelling a hollow utility pole that is particularly adaptedto be manufactured from a composite FRP in conformity with the conceptsof the present invention; and,

FIG. 16B is the remaining portion of the flow chart, a portion of whichis depicted in FIG. 16A, the FIGS. 16A and 16B being joined as depictedon those two FIGS.

DESCRIPTION OF AN EXEMPLARY EMBODIMENT

One representative form of a fiber-reinforced plastic utility poleembodying the concepts of the present invention is designated generallyby the numeral 10 on FIGS. 4 through 15 of the accompanying drawings.However, with initial reference to FIG. 1, a representative, prior art,utility pole 12 is constructed to have a length "L_(A) " above groundlevel "G" and a length "L_(B) " below ground level "G". It will beobserved that the thickness "T₁ " of the tip portion depicted in FIG. 3is greater than the thickness "T₂ " of the butt portion depicted in FIG.2. This is representative of prior art FRP utility poles.

The improved utility pole 10 is also constructed of fiber reinforcedplastic (FRP), and it may also have a length "L_(A) " above ground level"G" and a length "L_(B) " below ground level "G". The pole 10 is,however, distinctly comprised of a plurality of layers 14--three layers14_(A), 14_(B) and 14_(C) are shown in the representative pole depictedin FIG. 4. Each layer 14 is, in turn, comprised of one or more full, orpartial, circuits 16. In the representative pole 10, layer 14_(A)extends along the tip portion 18 of pole 10 and comprises a portion ofcircuit 16_(A). If required, as hereinafter explained, one or moreadditional circuits might be included in layer 14_(A).

Layer 14_(B) is comprised of the medial portion 20 of circuit 16_(A) inconjunction with a portion of circuit 16_(B), or any other circuit 16which might overlie the medial portion 20 of circuit 16_(A). Layer14_(C) is comprised of not only the entirety of circuit 16_(C) but alsothat portion of both circuits 16_(A) and 16_(B), as well as any and allother circuits which underlie circuit 16_(C). Here, too, one or moreadditional circuits 16 might be coextensive with circuit 16_(C), if suchcircuits are mathematically determined to be required, as is hereinaftermore fully explained. Each circuit 16 is comprised of two passes, ortraverses, 24A and 24B of resin-coated, reinforcing strands.

As previewed in the preceding paragraph, and as will appear in thedetailed description which follows, a particular structural member,component or arrangement may be employed at more than one location. Whenreferring generally to that type of structural member, component orarrangement a common numerical designation shall be employed. However,when one of the structural members, components or arrangements sodesignated is to be individually identified it shall be referenced byvirtue of a letter suffix employed in combination with the numericaldesignation employed for general identification of that structuralmember, component or arrangement. Thus, there are two passes--oneapplied in each direction--used to lay a circuit 16 of resin-coated,reinforcing strands, and those passes are generally identified by thenumeral 24, but the specific, individual passes--one in eitherdirection--are, therefore, identified as 24A and 24B, respectively, inthe specification and on the drawings.

On the other hand, when the structural members, components orarrangements are similar, but not exactly the same, a common numericaldesignation shall still be employed, but when the similar members,components or arrangements so identified are to be specificallydesignated, they shall be referenced by virtue of a letter subscriptemployed in combination with the numerical designation employed forgeneral identification of that structural member, component orarrangement. Thus, there are similar, but distinct, circuits, or cyclesformed by the two passes 24A and 24B. The circuits, or cycles, aregenerally identified by the numeral 16 but the specific, individualcircuits are, therefore, identified by the alphanumeric designations16_(A), 16_(B) etc. in the specification and on the drawings.

These same alphanumeric conventions shall be employed throughout thespecification.

Although the structure of the pole 10 is quite unique, the full flavorof its novelty is more likely to be appreciated if one considers how thenumber of layers are determined as well as how the length of the variouscircuits which combine to form those layers were determined. To bestunderstand that process one must refer to FIG. 16 and remember throughthe description that follows that the number and length of thesuccessive circuits are determined by computer-modelling, the algorithmof which is represented by the flow chart in FIG. 16.

The flow chart begins by arbitrarily selecting an original, maximumallowable stress "S_(max) ". It should be recognized that this valueneed not bear any realistic resemblance to what a true maximum allowablestress will eventually prove to be, as will hereinafter be more fullyexplained. Thus, one might select forty-thousand pounds per square inch(40,000 psi), which is fairly certain to exceed a realistic value for anFRP member.

The value of the original incremental adjustment "S_(incr) " by whichthe originally selected maximum allowable stress is to be adjusted,again as will be hereinafter more fully explained, is also selected. Thechosen value for the initial incremental adjustment is selected to besufficiently large that the binary chopping employed in thecomputer-modelling procedure will not take an overly extended period ofreal time to run but yet be sufficiently small that at least two testcycles will be required before the first binary chop is effected. Inaddition, if the maximum stress is initially selected to be higher thanreasonably anticipated for the ultimately determined maximum stress, thesign of "S_(incr) " should be negative. As such, an original value for"S_(incr) " might equal a minus eight thousand pounds per square inch(-8,000 psi). Note that these selections, while arbitrary in the sensethat they may not prove to be realistic, are intelligently chosen suchthat the values preferably initiate the computer-modelling by choosingan overly large "S_(max) " and a related value for "S_(incr) " to alloweffective binary chopping during subsequent stages of thecomputer-modelling routine.

Once these initial values are selected the ratio of the wall thicknessto the inside diameter (generally designated as the thickness/diameterratio) for the pole 10 is compared to a predetermined minimum value at asequential series of test stations 26 (FIG. 4). As a general rule, ithas been determined that the ratio required for an FRP utility pole isequal to, or greater than, 0.015.

The wall thickness is determined by finding the difference between theouter radius "r_(o) " of the wall and the inner radius "r_(i) " of thewall. That is, the thickness "t" may be mathematically expressed as

    t=(r.sub.o -r.sub.i)                                       (1)

This thickness is divided by the inner diameter "d_(i) " of the wall atthat test station 26 for which the ratio is being determined. Hence, theratio "R" may be mathematically calculated by the following equation:##EQU2## If the calculated ratio R_(C) is less than the minimum requiredratio R_(R), it is not acceptable, and another circuit 16 of FRP isdeemed to be applied from the butt portion 22 of the pole 10 to the teststation 26 at which R_(C) is being considered. Thereafter, the ratio isrecalculated. If the ratio is still not acceptable, an additionalcircuit is considered to have been added. This process is repeated untilthe R_(C) is equal to, or greater than 0.015.

In constructing a pole 10 having a significant overall length L_(o)--i.e.: the length L_(A) above ground level "G" plus the length L_(B)below ground level "G" --it has been found that seldom does only asingle circuit 16 (to form a single, full length layer 14) provide anacceptably strong pole. That is, it is seldom, if ever, satisfactory toprovide the same number of circuits at all test stations 26 along thefull length of the pole to provide the necessary strength for a pole. Tothe contrary, it has been determined that a plurality of layers 14 aregenerally required to provide the required thickness-to-diameter ratioR_(R).

After the required ratio R_(R) has been established at a test station,the pole 10 is analyzed to determine if the calculated stress S_(calc)at the test station 26 will equal or exceed the maximum stress S_(max)to withstand a cantilever load "F". The stress S_(calc) can bedetermined from the following equation: ##EQU3## where: M=the momentproduced by the rated load F_(R) ;

c=the distance from the neutral axis (centerline of the pole) to theouter surface of the pole, where the stress is maximum; and,

I=equals the moment of inertia--which is proportional to the differencebetween the outer diameter d_(o), raised to the fourth power, and theinner diameter d_(I), raised to the fourth power, for an annular crosssection.

That is: ##EQU4##

By virtue of having arbitrarily chosen an original S_(max) well inexcess of what would have been reasonably anticipated, it is expectedthat S_(calc) will be well below the originally selected S_(max) on theinitial run of the computer-modelling program at each test station 26above ground level "G". If not, an additional circuit will be added, asrequired.

In general, then, the stress will normally be minimum at the tip portion18 and increase as one considers the results at test stations 26progressively closer to the butt portion 22. A realistic structuraldesign for the pole can be achieved, for example, by placing the teststations at incrementally spaced locations along the length of the poleat approximately six inch (15.24 cm) intervals. When either thethickness ratio R is equal to or less than 0.015 or the calculatedstress S_(calc) exceeds the predetermined, maximum acceptable valueS_(max), another circuit 16 is added from the butt portion 22 to thetest station 26 where the calculation was made.

The calculations are repeated and required circuits 16 are added untilthe predetermined values required by the test formulas are achieved.

Tied in with the evaluation of the deflection when the pole is subjectedto deflection under the rated load F_(R) is the desirability todetermine that the columnar strength is sufficient for the pole beingconstructed. This will occur when a significant vertical load "P" isimposed on the pole. Readily recognizable vertical loads occur whenlarge lights, signs or transformers, either singly or in groups, aresupported symmetrically on the pole, but perhaps the most significantvertical loading is applied to utility poles by the use of guy wires.When vertical loading is considered, it has been found that thecantilever deflection load and the critical column load can generally beequated inasmuch as both of these are proportional to the product to themodulus of elasticity "E" multiplied by the moment of inertia "I". Acorrective factor must be included, however, as will be hereinafterexplained.

The wind load bearing capability of an FRP utility pole may becalculated by using the results from the cantilever load test specifiedin ANSI C136.20-1990. The test data consists of the distance L_(A) fromthe ground level "G" to the tip 18 of the pole 10, and the load at whichthe pole fails. All of the poles fail in buckling on thecompression-stressed side of the pole. This failure by buckling suggeststhat the poles may behave as columns, which fail in compressive bucklingduring cantilever load testing. Using column theory one is able topredict the failure load of the FRP poles from the load and deflectiondata, thereby establishing a non-destructive test which can be employedmathematically to ascertain the required thickness at each incrementallylocated station along the pole.

One can predict the deflection (δ) at the end of a cantilever beamsupporting a given load (in this case the rated load) by using theequation: ##EQU5## where: F_(R) =the rated load causing the beam todeflect;

a=the distance from the plane of fixation (ground level "G") to thepoint where the rated load F_(R) is applied to the beam;

L_(A) =the distance from the plane of fixation to the end of the beam;

E=the modulus of elasticity for the material from which the beam ismade; and,

I=the moment of inertia for the beam section.

Column theory predicts that the critical, or projected failure, loadF_(P) --i.e.:the buckling load--for a column with one end fixed andother end free can be mathematically estimated by the followingequation: ##EQU6##

Although it might appear that the term "EI" would be exactly the same inboth formulas 5 and 6 such that the solution of each equation for thatterm would then be equal to each other, it must be remembered that thederivation of formulas 5 and 6, as well as the operational ranges withinwhich each is intended to function are quite different--i.e.:the formulafor determining the deflection "δ" falls within the elastic limit of thematerial, but the critical., projected failure, load F_(P) falls outsidethe elastic limit. Perhaps of even greater importance, it should also benoted that FRP is not a homogeneous, isotropic material. Therefore, theflexural modulus of the FRP used in equation 5 may not be equal to themodulus used in predicting the critical load of a column. In addition,the pole is a tapered structure. As such, the "effective" moment ofinertia in bending may not be equal to the "effective" moment of inertiaused to predict the critical load of a column. Hence, a correctivefactor " B" must be introduced when equating mathematical expressions 5and 6 for mathematical propriety. Hence: ##EQU7##

Inasmuch as "a" equals L_(A), because both terms represent the distancefrom the point of fixation (the test station) to the point at which theload is applied--the point of final fixation is ground level "G"; hence"a" consistently equals L_(A) --one may solve for F_(P) and clear theexpression 0.25II² into the proportionality constant, expressed as "C"in the following equation: ##EQU8##

From equation (7) ##EQU9##

According to equation (8)--if one can determine the constant "C" and ifone knows: the length of the beam L_(A) ; the distance "a" from theground level "G" to the point at which the load "F" is applied; as wellas the deflection δ--one can mathematically predict the projectedfailure load F_(P). The terms "a", L_(A), F_(R) and δ are readilyascertained. However, one must determine "C" from test data.

For the purposes of the present invention, the evaluation of "C" wasaccomplished by using pile load and deflection test data. That analysisused the deflection at a test load of 300 pounds to evaluate "C." Usingthat test load minimized the affects of inconsistencies in thedeflection measurements at low loads, and it also minimized the effectsof the ground line strap stretching in the test facility.

To identify a linear relationship between the load/deflection parameterand the failure load, data for "a", L_(A) and the deflection δ resultingfrom a three hundred (300) pound load was entered into a spreadsheet,and the load-deflection parameter was computed. A linear regressionanalysis of the failure load versus the load-deflection parameter,extending through the origin of a graphical representation thereof,yielded a value of -0.0843 for "C" within a standard error estimate of270 pounds for the failure load and a correlation coefficient (r²) of0.94 (unity being a perfect data fit). It must be understood that thedeflection test data was based on the use of glass reinforcing fiberhaving a "yield" of two hundred, fifty (250) yards of the glass filamentfrom one pound of glass. It should be recognized that different fibersor even glass fibers produced at a different yield rate might result ina different value of "C". The results of the calculations confirmed theapproach described herein to manufacture hollow, tapered utility poleswithin the concept of the present invention.

In summary, after the wall thickness to the inner diameter ratio and thestress checks have been completed at each test station along the lengthof the pole above ground, the tip deflection δ at the rated load isdetermined, and the projected failure load F_(P) at that deflection δ iscalculated in accordance with formula (8). If the rated load F_(R) isnot less than the projected failure load F_(P) and if the projectedfailure load F_(P) is not less than the rated load F_(R) plus apreselected constant value ε, the maximum allowable stress S_(max) isrevised.

Before detailing an explanation as to how the maximum allowable stressis revised, it should be explained that in the comparison of the ratedload to the projected failure load, the rated load F_(R) is thepublished horizontal load for the class of pole being manufactured plusa value based on the standard error estimate of two hundred, seventy(270) pounds, increased to four hundred (400) pounds for an additionalmargin of safety. Hence, if the class of pole is rated as withstanding ahorizontal load of two thousand four hundred (2,400) pounds, the ratedload would be two thousand, eight hundred (2,800) pounds. The factor εis a minimum constant which may be on the order of about one hundred(100) pounds in order to assure the spread necessary to allow either a"yes" or a "no" response to the question of whether F_(R) <F_(P) <F_(R)+ε.

In the situation where the maximum allowable stress S_(max) requiresrevision, a "no" answer will result and then one must ascertain whetherthe incremental stress S_(incr) should be added to the then existingvalue for S_(max) or be subtracted therefrom. That determination is doneby evaluating whether: ##EQU10## where "i" is the current iteration ofthe calculations to evaluate tip deflection at the rated load F_(R) aswell as to determine the projected failure load F_(P) at thatdeflection. Hence, the expression "i-1" designates the previousiteration. A counter may be incorporated in the computer-modellingprogram to identify the successive iterations.

On the first run of the computer-modelling program there is no "i-1"iteration, and the stated expression (10) will, therefore, provide thecomputer with zero for an answer inasmuch as dividing zero by any valueresults in an answer of zero.

In either event, the expression (10) would result in a number greaterthan, or equal to, zero so the "no" branch of the flow chart isfollowed, and a new S_(max) will be determined by adding the currentincremental value S_(incr) to the current, or original, S_(max).Inasmuch as the initially set incremental stress value was designated asa minus number, the new maximum allowable stress S_(max) will be theprevious maximum allowable stress minus the incremental stress S_(incr).That new maximum stress S_(max) will then be reset in the top box of theflow chart, and the calculations described in the flow chart aresuccessively recalculated. On the second, and all successive, iterationsthe test delineated as mathematical expression (10) is recalculated, anda current as well as a previous value for F_(R) and F_(P), exists toprovide a numerical value for the mathematical test expressionidentified as formula (10). The iterations are continued and new S_(max)are reset at the conclusion of each cycle.

At some iteration the test ratio established by expression (10) becomesless than zero so the "yes" branch of the flow chart is followed. Whenthe "yes" answer is obtained, the incremental stress S_(incr) isdecreased by one half (1/2), and the sign of the incremental stressS_(incr) is changed.

The aforesaid modelling formulas are continued at all above ground level"G" stations 26 until the test F_(R) <F_(P) <F_(R) +ε is answered "yes".At that point the below ground level evaluation occurs. Under normalcircumstances that portion of the pole which extends below ground levelis not changed, and the program is terminated. However, an evaluationstep is provided in the event some special circumstances require specialtreatment.

When the computer-modelling of the pole 10 is completed, the resultingpole configuration, for example, may be as follows. At test station26_(A), the moment of inertia is a function of the diameters d₀₁ andd_(I1) of the circuit 16_(A) which comprises passes 24A₁ and 24B₂, andthe distance c is equal to c₁. It will be appreciated that the diameterswill continue to increase due to the taper of the mandrel and thethickness varies as a result of wrapping the resin-coated, fiber strandson a tapered mandrel. As such, the calculations continue until the poleis completed.

At test station 26_(B) the moment of inertia is a function of thediameters d_(o2) and d_(I2) the distance c is equal to c₂. In any event,at test station 26_(B) at least one of the tests failed, and circuit16_(B) --comprising two passes 24A₂ and 24B₂ --was added.

Circuit 16_(B) need not extend beyond test station 26_(B), and layer14_(A) thus constitutes only that portion of the circuit 16_(A) thatextends from test station 26_(B) to and including the tip portion 18.

At test station 26_(C), diameters d_(o3) and d₁₃ were used, as was c₃.However, no additional circuit 16 was required. On the other hand, attest station 26_(D) --where diameters d_(o4) and d_(I4) were used, aswas c₄, to calculate the mathematical tests--an additional circuit16_(c) comprising passes 24A₃ and 24B₃ was required.

At test station 26_(E), however, all tests continued to pass and nofurther circuit 16 was required. Accordingly, the pole 10 thus has afirst layer 14_(A) which extends from the tip portion 18 to test station26_(A) ; a second layer 14_(B) that extends between test stations 26_(B)and 26_(D) ; and, a third layer 14_(c) that extends from test station26_(D) to the butt portion 22.

By utilizing a conventional digital computer programmed to calculate therequired values, the process is simplified and can be completed in anacceptable time period for different length poles and for various loads.The loads will vary due to the situation in which the pole will be used.For example, the pole may support lights, signs, transformers--or bestabilized by guy wires--all of which might impose a cantilever load. Itis also necessary to consider the prevailing winds and the maximumpossible wind load that might occur at the location the pole is tooccupy.

After the mathematical, computer-modelling of the pole is completed, thepole is actually fabricated in conformity with the number and lengths ofthe circuits determined by the modelling technique. As seen in FIG. 15,the circuits 16 of the resin-coated, fiber reinforcing strands 32 arelaid-up on a mandrel 28 which may be rotatably supported on itslongitudinal axis 30. The first pass 24A of each circuit 16 is placed onthe mandrel 28 such that the fiber reinforcing strands 32A are disposedat a right hand helical angle Θ_(R) while the second pass 24B of eachcircuit 16 is placed on the mandrel 28 such that the fiber reinforcingstrands 32B are disposed at a left hand helical angle Θ_(L). Preferablythe angles Θ_(R) and Θ_(L) have the same absolute value but are oppositein direction. Successive circuits will apply the resin-coated,reinforcing strands 32 at comparable helical angles. A value of fifteendegrees (15°) has been found to be acceptable for most conditions towhich a utility pole will be subjected.

Inasmuch as the pole structure can be determined by computer-modelling,without actually constructing the pole, the inner circuits applied tothe mandrel 28 can be the shorter circuits. Thus, one could wind thecircuit 16_(c) first, and it would, therefore, be the innermost circuit.A pole made in this manner would present a generally smooth, outersurface and perhaps have a more pleasant aesthetic appearance.

The foregoing detailed description of an exemplary embodiment of the aFRP utility pole has been presented for the purposes of illustration anddescription. It is not intended to be exhaustive nor is it intended tolimit the invention to the precise form disclosed. Obviousmodifications, or variations, are possible in light of the aboveteachings. The embodiment was chosen and described to provide the bestillustration of the principles of the invention and its practicalapplication in order to enable one of ordinary skill in the art toutilize the invention in various embodiments and with variousmodifications as are suited to the particular use contemplated. All suchmodifications and variations are within the scope of the invention asdetermined by the appended claims when interpreted in accordance withthe breadth to which they are fairly, legally and equitably entitled.

While only a preferred embodiment of the present invention is disclosed,it is to be clearly understood that the same is susceptible to numerouschanges apparent to one skilled in the art. Therefore, the scope of thepresent invention is not to be limited to the details shown anddescribed but is intended to include all changes and modifications whichcome within the scope of the appended claims.

As should now be apparent, the present invention teaches that an FRPutility pole embodying the concepts of the present invention, as well asthe method disclosed for making such a pole, are fully capable ofachieving the objects of the invention.

We claim:
 1. A method of computer-modelling a hollow utility pole forsubsequent manufacture from a composite FRP, the utility pole having abutt portion, a medial portion and a tip portion, said method comprisingthe steps of:determining the length of the pole to be fabricated;selecting a mandrel having a representative diametral configuration anda length to accommodate the full length of the pole from the buttportion to the tip portion; establishing test stations spacedincrementally along the mandrel from the location where the tip portionwill be formed to the location where the butt portion will be formed;simulating the application of resin-coated, fiber reinforcing strands ina circuit from the location of the butt portion to the location of thetip portion; selecting fifteen thousandths (0.015) as thethickness-to-diameter constant; determining, at a test station closestto the tip portion of the pole, if the thickness-to-diameter ratio forthe wall thickness of the circuit of resin-coated, fiber reinforcingstrands is equal to or less than an established constant; simulating theapplication of additional circuits of resin-coated, reinforcing strandsas are necessary to satisfy the thickness-to-diameter ratio at the firsttest station; and, determining if the thickness-to-diameter ratio on thenext successive test station is equal to or greater than the establishedconstant; simulating the application of additional circuits ofresin-coated, reinforcing strands as are necessary to satisfy thethickness-to-diameter ratio at the next successive test station; and,continuing the testing steps and the simulation of additional circuits,as needed, at each test station until the thickness-to-diameter test hasbeen satisfied along the selected length from the tip portion toward thebutt portion.
 2. A method of modelling a hollow utility pole, as setforth in claim 1, comprising the further step of:selecting fifteenthousandths (0.015) as the thickness-to-diameter constant.
 3. A methodof modelling a hollow utility pole, as set forth in claim 1, comprisingthe further steps of:determining if the acceptable stress resistanceunder a predetermined load calculated at the successive test stations isgreater than the stress resistance required for each respective teststation; and, simulating the application of additional circuits ofresin-coated, reinforcing strands as are necessary to satisfy therequired stress resistance at each station before proceeding.
 4. Amethod of modelling a hollow utility pole, as set forth in claim 3,comprising the further step of:calculating the stress resistance at eachstation by virtue of the formula: ##EQU11## where: M=the moment producedby a selected load; c=the distance from the neutral axis of the pole tothe outer surface thereof; and, I=the moment of inertia for the crosssection of the pole at the test station.
 5. A method of modelling ahollow utility pole, as set forth in claim 4, comprising the furthersteps of:evaluating the tip deflection at each station when thesimulated pole is subjected to the rated load; projecting the failure.load from the tip deflection at each station; adjusting the maximumstress when the rated load is greater than the projected failure load;determining if the calculated stress resistance is less than theadjusted maximum stress; and, simulating the application of additionalcircuits of resin-coated, reinforcing strands as are necessary to assurethat the calculated stress is less than the adjusted maximum stressbefore proceeding.
 6. A method of making a hollow utility pole, as setforth in claim 5, comprising the further step of:calculating theprojected failure load at each station by virtue of the formula:##EQU12## where F_(R) =the rated load causing the beam to deflect; F_(P)=the projected failure load; a=the distance from the plane of fixationto the point where the rated load F_(R) is applied to the beam; L_(A)=the distance from the plane of fixation to the end of the beam; C=theproportionality constant; and, δ=the deflection of the beam under theapplied load.
 7. A method of making a hollow utility pole, as set forthin claim 6, comprising the further steps of:arbitrarily selecting amaximum allowable stress that is preferably higher than anticipated;and, selecting an incremental stress for adjusting said maximum stresswhen the test F_(R) <F_(P) <F_(R) +ε is not satisfied.
 8. A method ofmaking a hollow utility pole, as set forth in claim 6, comprising thefurther step of:determining the proportionality constant using a linearregression analysis of the failure load versus the load deflectionparameter.
 9. A method of making a hollow utility pole, as set forth inclaim 7, comprising the further step of:determining a new incrementalstress for resetting said maximum allowable stress with a binarychopping routine if the test ##EQU13## is satisfied.
 10. A method ofmaking a hollow utility pole, as set forth in claim 8, comprising thefurther step of:substituting a negative eight hundred, forty-three tenthousandths (-0.0843) for the proportionality constant if glassreinforcing fibers having a yield of two hundred and fifty (250) yardsper pound of glass are employed.
 11. A method of making a hollow utilitypole from the computer-modelling technique, as set forth in claim 10,comprising the further steps of:applying resin-coated, fiber reinforcingstrands over a mandrel; and, curing the resin to complete the pole. 12.A method of making a hollow utility pole having a butt portion, a medialportion and a tip portion, said method comprising the stepsof:determining the length of the pole to be fabricated; selecting amandrel having a representative diameter and length on which to make thepole; establishing test stations spaced incrementally from the tipportion to the butt portion; applying resin-coated, fiber reinforcingstrands over the mandrel; determining, at each of said test stations, ifthe thickness-to-diameter ratio for the wall thickness of theresin-coated, fiber reinforcing strands laid on said mandrel is equal toor less than 0.015; applying additional circuits of resin-coated,reinforcing strands as are necessary to satisfy thethickness-to-diameter ratio at the first test station; calculating thestress resistance at each of said test stations by virtue of theformula: ##EQU14## determining if the acceptable stress resistance undera predetermined load calculated at said same test station is greaterthan the stress resistance required for said test station; applyingadditional circuits of resin-coated, reinforcing strands as arenecessary to satisfy the required stress resistance at said test stationbefore proceeding; calculating the critical load at each of said teststations by virtue of the formula: ##EQU15## determining if the actualloading to be applied to the pole is lower than the critical load atwhich the pole would buckle at said station; adjusting the acceptablestress if the preselected, rated load is not less than the projectedfailure load and the rated load does not exceed the projected failureload by a predetermined margin of safety; applying additional circuitsof resin-coated, reinforcing strands as are necessary to assure that thecalculated and adjusted maximum stresses satisfy the margin of safetycriterion; continuing the testing and applying steps at each teststation until the pole is satisfactorily laid up on the mandrel; and,curing the resin to complete the pole.
 13. A method of making a hollow,utility pole, as set forth in claim 12, wherein:the step of determiningif the thickness-to-diameter ratio is satisfied is accomplished at alltest stations before proceeding with the remaining steps of the process.14. A method of making a hollow, utility pole, as set forth in claim 13,comprising the further steps of:recalculating the thickness-to-diameterratio at all test stations after any additional circuits are determinedto be necessary as a result of any of the remaining steps of theprocess.
 15. A method of computer-modelling a hollow utility pole forsubsequent manufacture from a composite FRP, the utility pole having abutt portion, a medial portion and a tip portion, said :methodcomprising the steps of:determining the length of the pole to befabricated; selecting a mandrel having a representative diametralconfiguration and a length to accommodate the full length of the polefrom the butt portion to the tip portion; establishing test stationsspaced incrementally along the mandrel from the location where the tipportion will be formed to the location where the butt portion will beformed; simulating the application of resin-coated, fiber reinforcingstrands in a circuit from the location of the butt portion to thelocation of the tip portion; determining, at a test station closest tothe tip portion of the pole, if the thickness-to-diameter ratio for thewall thickness of the circuit of resin-coated, fiber reinforcing strandsis equal to or less than an established constant; simulating theapplication of additional circuits of resin-coated, reinforcing strandsas are necessary to satisfy the thickness-to-diameter ratio at the firsttest station; and, determining if the thickness-to-diameter ratio on thenext successive test station is equal to or greater than the establishedconstant; simulating the application of additional circuits ofresin-coated, reinforcing strands as are necessary to satisfy thethickness-to-diameter ratio at the next successive test station;continuing the testing steps and the simulation of additional circuits,as needed, at each test station until the thickness-to-diameter test hasbeen satisfied along the selected length from the tip portion toward thebutt portion; determining if the acceptable stress resistance under apredetermined load calculated at the successive test stations is greaterthan the stress resistance required for each respective test station;simulating the application of additional circuits of resin-coated,reinforcing strands as are necessary to satisfy the required stressresistance at each station before proceeding; calculating the stressresistance at each station by virtue of the formula: ##EQU16## where:M=the moment produced by a selected load;c=the distance from the neutralaxis of the pole to the outer surface thereof; and, I=the moment ofinertia for the cross section of the pole at the test station;evaluating the tip deflection at each station when the simulated pole issubjected to the rated load; projecting the failure load from the tipdeflection at each station by virtue of the formula: ##EQU17## whereF_(R) =the rated load causing the beam to deflect;F_(P) =the projectedfailure load; a=the distance from the plane of fixation to the pointwhere the rated load F_(R) is applied to the beam; L_(A) =the distancefrom the plane of fixation to the end of the beam; C=the proportionalityconstant; and, δ=the deflection of the beam under the applied load;determining the proportionality constant using a linear regressionanalysis of the failure load versus the load deflection parameter;substituting a negative eight hundred, forty-three ten thousandths(-0.0843) for the proportionality constant if glass reinforcing fibershaving a yield of two hundred and fifty (250) yards per pound of glassare employed; adjusting the maximum stress when the rated load isgreater than the projected failure load; determining if the calculatedstress resistance is less than the adjusted maximum stress; and,simulating the application of additional circuits of resin-coated,reinforcing strands as are necessary to assure that the calculatedstress is less than the adjusting maximum stress.
 16. A method of makinga hollow utility pole from the computer-modelling technique, as setforth in claim 10, comprising the further steps of:applyingresin-coated, fiber reinforcing strands over a mandrel; and, curing theresin to complete the pole.
 17. A method of modelling hollow utilitypole, as set forth in claim 4, comprising the steps of:evaluating thetip deflection at each station when the simulated pole is subjected tothe rated load; projecting the failure load from the tip deflection ateach station; and, simulating the application of additional circuits ofresin-coated, reinforcing strands as are necessary to assure that therated load is less than the projected .failure load before proceeding.